Practical significance of the kinetics of heterotrophic oxidation and endogenous respiration in activated sludge plants

Transcription

1 Practical significance of the kinetics of heterotrophic oxidation and endogenous respiration in activated sludge plants H B Tench The Windings, College Rd., Spinkhill, Sheffield, S21 3YB henry@tench.org Abstract The work in this paper has been evolved to explain the variation in surplus sludge production and in the rates of endogenous respiration in the non-nitrifying activated sludge plants at Manchester which had different numbers of compartments. In multi-compartment plants, the high oxygen demand for substrate oxidation in the initial compartments exceeds the oxygen supply so that they are partially anoxic. As a result, the average endogenous respiration and oxygen demand decrease with increase in the number of compartments so that carbon oxidation and power consumption are reduced. The higher proportion of biomass in the mixed liquor suspended solids (MLSS) makes it possible to produce higher quality effluents. Any biomass higher than the minimum necessary to fully use the supplied oxygen in the last compartment, is anoxic. A computer simulation using Michaelis-Menten mixed order kinetics, is developed to calculate the changes in endogenous respiration. This gives good agreement with the Manchester endogenous respiration rates when using a half saturation (Michaelis) constant determined respirometrically under conditions of high turbulence. Values for the half saturation constant reported by other researchers are lower and possible reasons for this are suggested. Keywords Heterotrophic oxidation, Michaelis-Menten kinetics, endogenous respiration, power saving. INTRODUCTION The mixed order Monod equation is generally considered to describe the rate of heterotrophic oxidation though Kroiss and Ruider (1977) have shown that the oxygen uptake rate in a full scale plant followed a first order course. As has been confirmed by numerous investigators, Pasveer (1953) demonstrated that oxygen supply in full scale plants is the rate limiting step in the heterotrophic oxidation process. Also, because the rate of oxygen supply is proportional to the dissolved oxygen (DO) deficiency, full scale plants need to operate with DO s which are at or below the point where the rate of reaction becomes independent of the DO. The reason for the big differences in the biomass which could be grown per unit load which were found for three Manchester plants with differing intensities of aeration has been obscure, (Tench, 1968), but can be explained by applying the above kinetic constraints to the differing numbers of compartments in the plants. The reaction rate is based on the Michaelis-Menten rather than the Monod equation because it has a usable theoretical biochemical basis which is briefly described and further developed in Appendix 2. As it has been shown by Hearon (1952) to apply to chains of enzymes, it is a reason for the success of the similar but pragmatic Monod equation, for which no reliable theoretical basis has been found (Liu, 2007). If the rate of growth of biomass is proportional to the rate of oxidation of substrate then the Michaelis half saturation constant, K m, is proportional to the Monod constant, K S. Even though sewage is a complex mixture of solid and colloidal particles and soluble compounds, the Michaelis-Menten relationship has been proved, using a Warburg Respirometer, to apply to sewage and to a range of single substrates with results appropriate to the entry position for their oxidation in the enzyme chains (Tench and Morton, 1962).

2 The rapid clarification of sewage when it is mixed with activated sludge is no doubt partly due to adsorption of inert and slowly oxidisable solid and colloidal particles, but the readily oxidisable substrates which can include solids (Water Pollution Research Laboratory Annual Report, 1962), react with the enzyme chains within the floc to form biomass/substrate complexes in accord with Michaelis-Menten theory. The biomass apparently has the capacity to absorb most of the applied substrate so that the reaction rate approaches a maximum which is first order with respect to the substrates in the sewage. In each compartment of a plant the rate at which the Michaelis-Menten biomass/substrate complex decomposes is governed by the oxygen supply which limits the load removal and it is only in the final compartment that the sludge has sufficient capacity to absorb the oxidisable substrate load on recycle back to the plant inlet. The slowly oxidisable solids will accumulate in the sludge until the rate of hydrolysis and oxidation plus wastage equals the rate of adsorption. In practice, the Michaelis-Menten assumption that the substrate is so much in excess of the enzyme that its concentration is unchanged when the two are mixed cannot be guaranteed. To ensure that mixed order kinetics applied in the Manchester tests, the oxygen demand of the sewage was increased tenfold by evaporation and it was shown that this did not alter the total demand MICHAELIS-MENTEN THEORY APPLIED TO COMPARTMENTS IN SERIES Nomenclature S substrate oxygen demand in E 1,2.N each compartment, ML -3 S FE S S S ST t t1,2.n N X H X HS R substrate oxygen demand in final effluent, ML -3 sewage substrate oxygen demand, ML -3 stored substrate oxygen inert material in sludge, ML -3 equilibrating rate constants oxidation reaction rate constant, T -1 Michaelis Constant, ML -3 demand, ML -3 K m k 2 k 3 hydraulic detention time, T hydraulic detention time in reference plant, T hydraulic detention time in each compartment, T number of compartments in plant heterotrophic biomass, ML -3 biomass/substrate complex in reference plant, ML -3 active mass/substrate complex X I k 1, k 2 k 3 b H aer O 2 X HS 1,2.N F v k 3 X HS V k 3X H rate of substrate oxidation, ML -3 T -1 maximum rate of substrate oxidation, ML -3 T -1 endogenous respiration rate constant, T -1 aerobic fraction total oxygen demand (equals oxygen supply), ML -3 T -1 endogenous/substrate in each compartment, ML -3 oxidation ratio Basis of the simulation A single compartment activated sludge plant with an oxygen supply which provides just sufficient dissolved oxygen, (DO), to maintain fully aerobic conditions in the sludge floc is used as a reference. Splitting into several compartments makes the initial ones partially anoxic and the aerobic fraction is determined by comparing the oxygen demand in each compartment with the fully aerobic reference plant. k 1

3 The Michaelis-Menten equation is normally quoted as K m S but as the velocity of reaction, v, depends on the concentration of biomass/substrate complex (which is an intermediate compound formed between the enzyme and its substrate) it can be restated as: (1) where k 3 is the rate constant for the oxidation reaction. In the single compartment reference plant the rate of oxidation of substrate is k 3 X HS R and in accord with Michaelis-Menten theory this equals: K m S FE and the rate of load removal of, is also equal to this, so that (2) In the partially aerobic first compartment of a multi-compartment plant oxidation only occurs in the fraction which is aerobic so that the similar relationship here is: There is no known way of determining the values of k 3 and X H, but this difficulty can be overcome by proportioning equations (2) and (3), which eliminates both of these parameters: Rationalising gives: The degree of oxidation of substrate and the value of the aerobic fraction,, depend upon the rate of oxygen supply, O 2, and in the fully aerobic reference plant, this equals the total of the demands for endogenous respiration and substrate oxidation, so that: To be dimensionally correct the rate of endogenous respiration in this equation has to be in the same units as the rate of substrate oxidation and thus, to determine how the supplied oxygen is used it is necessary to represent it as a proportion of the substrate load. Putting changes the equation to: (5) As shortage of oxygen affects the rate of endogenous respiration as well as substrate oxidation, the relation between the oxygen supply and the demand in the first compartment of a plant containing N compartments is given by: t 1. Rearranging this equation gives: (6) For any rate of oxygen supply, the value of the aerobic fraction in this compartment can thus be deduced by inserting assumed values of S in the simultaneous equations (4) and (5) and solving for written as: iteratively until a value which satisfies both equations is found. Equation (6) can be (3) (4), and summing this for all compartments at a constant oxygen supply, gives:, where k 3 X HS k 3 X H S FE aer 1 O 2R bx H O 2 R aer 1 aer 1 E 1 av aer bx H + S S S FE k 3 X H S K m S k 3 X H S FE K m S FE S S S FE aer 1 k 3 X H S E 1 K ms E 1 S S S E 1 t 1 S F E K m S E 1 aer 1 S E 1 K m S FE S FE K m S E1 S S S E1 S E 1 K m S FE S S S FE t 1 F S S S FE (1+F ) S S S FE O 2 N S S S E 1 F S S S FE S S S FE t 1 S S S t E1 R O2 N aer 1 F S S S FE t 1 O2 N t 1 aer 1 F S S S FE t 1 S S S E 1 av O 2 N 1 aer F S S S FE aer 1 aer 2... aer N / N S S S FE v V S S S S E 1 aer 1 for compartments of equal size.

4 For known values of S S and S FE, the oxygen supply needed to satisfy the demand in the reference compartment is calculated using the selected value for F. Using this same value, the oxygen supply required for several compartments is assumed and applied to the first compartment so that the load removed can be calculated from equations (4) and (6). The resulting value for S E 1 is then the feed to the second compartment and the process is repeated until S FE is determined. The assumed oxygen supply rate is then varied until the required final effluent is achieved. This can be done on a spreadsheet but for convenience a computer programme has been developed to undertake the necessary iterative convergent calculations. As the oxygen used for substrate oxidation is constant, endogenous respiration is calculated by difference. As the load removed in the last compartment of a multi-compartment plant is less than that in the single compartment it follows from equation (2) that for the same quality of effluent, the rate of oxidation has to be restricted by lack of oxygen. Alternatively, the rate can be restricted by reducing X H to make the sludge in this last compartment fully aerobic. The biomass is then the minimum needed for full treatment as further decrease would lead to incomplete use of the available oxygen. At this minimum, the sludge in the initial compartments is partially anoxic and the biomass grown as the purification proceeds adds to the anoxic portion and does not increase the rate of substrate oxidation. As higher concentrations of biomass have no significance, this critical level is the only satisfactory basis on which to proportionate changes in endogenous respiration and heterotrophic oxidation rates resulting from changes in oxygen supply. As the critical biomass is proportional to the load removed in the last compartment, it reduces with increase in the number of compartments and increases with increase in rate of aeration and load. EXPERIMENTAL EVIDENCE The two Simplex plants used in the determinations of biomass maxima have been described by McNicholas and Tench, (1959) and the Bioaeration plant (Bio) by Tench, (1996). The Bioaeration plant was a plug flow plant with internal recirculation; the Simplex No.2 (Sx2) plant was divided into three sections in sequence and the Simplex No.1 (Sx1) plant was a single compartment. The loads treated by the plants were different but this does not affect the development of the theory. In the tests the 5-day BOD was used as it has advantages over COD in that it does not significantly include slowly oxidisable material which can take very many days to be fully expressed or inert material which was particularly important at Manchester for at the time of the tests, the sewage contained about 40% of trade wastes containing inert organic chemicals. The substrate load has been calculated from the average sewage feed of 221mg/l as 5-day BOD and the effluent of 21mg/l from the Sx1 plant. A value for the oxygen uptake by endogenous respiration in the reference plant has to be assumed and as discussed in Appendix 1, a three day sludge age criterion indicates that it is about equal to the oxygen demand for substrate oxidation so that F b X H k 3 X HS 1.0. However as the precise value is uncertain, extreme values for F of 0.5 and 1.5 were tested and it was found that the results were not sensitive to this figure. The value of K m for the Manchester sewage was determined respirometrically to be 259mg/l of applied 5-day BOD and was the same for all three plants. Theoretically this could include some element of storage and was actually K m +S ST where S ST is the stored BOD, but it could still be a low side estimate because the maximum shaking rate used in the Warburg Respirometer was perhaps not high enough to fully express the oxygen demand, (Tench and Morton, 1962). Accordingly, the

5 predicted changes in endogenous respiration in plants with up to 12 compartments are plotted in Figure 1 for the much larger K m of 3000mg/l as well as for 259 mg/l and the much smaller one of 20mg/l quoted as typical in ASM1 (Henze et al, 1986). In all cases a quite rapid initial reduction tends to an asymptote as the number of compartments is increased. Fig 1 - Predicted change in endogenous respiration with increase in no. of compartments as a fraction of that in a single compartment plant with effluent of 21mg/l BOD As the rate of oxygen supply is proportional to the DO deficiency, it follows that it is higher than average in the initial compartments due to the high demand drawing down the DO. An estimate of this can be made (Tench, 2008a) but it appears to have only a marginal effect and could be offset by change in alpha factor and so has not been taken into account in preparing Figure 1. It is shown in Appendix 1 that the endogenous decay rate in a plant is equal to the rate of growth of biomass divided by the maximum biomass which can be grown in it. The loads treated by the plants and thus the biomass growth, were in the proportions: 1(Bio): 2.19(Sx2): 4.93(Sx1). However, as was shown by measurement of nitrogen content in around 170 samples from each plant and also from oxygen uptake measurements, (Tench, 1968, 2003, 2008) the maximum biomasses which could be grown in them were in the proportions: 1(Bio): 1.67(Sx2): 1.92(Sx1). differences between these two sets of ratios are quite marked and taking the ratios between them indicates that the endogenous rate and thus the aerobic fractions, changed in the proportions: 1(Bio): 1.31(Sx2): 2.57(Sx1). It appears that the aerobic fraction for the Bio was 0.39 of that for the single compartment Sx1 as their average final effluents were identical. This figure does not fit any prediction made for a K m of 20mg/l but indicates that the configuration of this hybrid flow plant may have been equivalent to a plant having about 5 compartments for a K m value of 259mg/l which conclusion would not be greatly changed if K m were taken to be 3000mg/l. The effluent from the 3-compartment Sx2 plant was better than that from the other two plants and averaged 18mg/l BOD. This improvement in the average effluent quality requires an increase in aeration to increase the aerobic biomass. If the biomass was below the critical level for this effluent quality and the improvement was entirely due to an increase in aeration, then the increase would have been 8% which would unnecessarily increase in DO in the last compartment. However, an The

6 increase in biomass of 11% would have reduced the necessary extra oxygen supply to 4% and the DO deficiency in the last compartment would then have been the same as in the reference plant. The theory predicts that these scenarios would respectively increase the average endogenous respiration rate in the Sx2 plant to either 0.49 or 0.50 of that in the Sx1 plant, both of which are close to the 0.51 found in practice. A value corrected to 21mg/l BOD is shown in Figure 1. DISCUSSION Other plant performance data are consistent with the theory. Over a three year period the hybrid flow Bio produced an average of 0.86 kg solids/kg BOD whereas the 3-compartment Sx2 plant produced 0.80kg solids/kg BOD and the single compartment Sx1 plant produced 0.65 kg solids/kg BOD, (Tench, 1968). Also, the DO in the Sx1 was typically 4.0mg/l which high figure confirms that the floc was fully aerobic as required by theory. If the improved effluent in the Sx2 was due to the 8% increase in aeration postulated above, then the DO deficiency in the last compartment was 86% of the optimum in the reference plant. The optimum DO will depend on the demand exerted by the floc but it is generally accepted that it is at, or below, 1.0mg/l. Assuming it to be between 0.5mg/l and 1.0mg/l in the reference plant gives a prediction of 1.8 to 2.2mg/l for the DO in the Sx2 last compartment which is broadly consistent with the actual DO, typically found to be in the range 2.0 to 2.5mg/l. The DO s for the Bio were in the range 0.9 to 1.2mg/l. As can be seen from the ratios between the loadings dealt with by the three plants of 1(Bio): 2.19(Sx2): 4.93(Sx1), the Simplex plants were more intensively aerated than the Bio and for the same result to be achieved with maximum use of the available oxygen, the ratio between the biomasses held should theoretically have been the same. However, in practice the MLSS in the plants averaged 2000, 3200 and 4000mg/l in order to equalise the nitrogen content and thus the proportion of biomass. The resulting biomass ratios of 1(Bio):1.6(Sx2): 2.0(Sx1) were not in proportion to the loadings and it appears that the high DO s in the Simplex plants arose because the biomasses in those plants were below the critical level necessary for best results. The most important prediction from the theory is that the average rate of endogenous respiration and the oxygen supply necessary decreases with increase in the number of compartments. As is clear from Fig. 1, the extent of the predicted decrease depends on the value of the selected K m. The value of 20mg/l as COD for the half saturation constant was determined by Dold et al (1980) and is in line with a number of laboratory studies in which it has been found that the rate of removal of single substrates was zero order, which indicates a low value for the half saturation constant, (e. g., Water Pollution Laboratory Annual Report, 1962). As detailed experimental conditions are not given, the reason for the low figure cannot be identified but it may have been obtained under conditions of low turbulence. However, Pasveer (1953) suggested that turbulence in full scale plants reduces floc size and so increases its aerobicity. That turbulence had an effect on oxygen uptake was confirmed in the Manchester experiments as it was found that the rate of respiration increased with increase in the shaking rate in the respirometer and accordingly high rates were employed in order to maximise the oxygen uptake. As shown in Appendix 2, a low rate of oxygen diffusion into the floc could lead to a low estimate for the value of K m. However, the oxidation of colloidal and other solids no doubt occurs at the floc surface and if so, the effect of turbulence would be to increase the reaction rate by increasing the available surface area. It should be possible to decide between these alternatives experimentally but whatever the reason it appears that turbulence significantly affects the value of K m (and also of V), with possible practical as well as theoretical, consequences. It appears possible to save power by reducing the endogenous respiration needed to reach the required effluent standard. It follows from equation (1) that the rate of endogenous respiration

7 increases exponentially relative to the linear increase in rate of load removal as the substrate concentration decreases. The continuously variable load on a wastewater treatment plant produces variability in the aerobic fraction and thus in the effluent and endogenous respiration. A constant effluent quality would be produced and the endogenous respiration minimised, if the aerobic biomass were varied to suit the load to be removed. The necessary decrease at low loads can only be achieved by reducing the oxygen supply, with or without reducing the return sludge rate to reduce the MLSS. Alternatively, part of the plant can be closed and the sludge allowed to settle at times of low load, as was practised at the Halifax surface aeration plant in the 1950 s (Lumb, 1959). In nitrifying plants the need to prevent wash out of nitrifiers increases the MLSS and thus the proportion of anoxic sludge which explains why nitrification and denitrification can simultaneously occur in the initial compartments. The theory provides a way to quantify this effect, but changes in oxygen supply due to changes in alpha factor and in DO deficiency may need to be taken into account. No data for the Manchester sewage is available as the chemical content inhibited the process to such an extent that there was no trace of nitrification even with the sludge ages of up to the average of 11 days used to check the validity of the biomass/mlss relationship. CONCLUSIONS 1. A theory based on Michaelis-Menten mixed order kinetics has been found to explain the variation in biomass in three plants at Manchester. Subdivision of an aeration tank into an increasing number of compartments increases the oxygen demand relative to the oxygen supply in the initial compartments and produces partially anoxic conditions so that endogenous respiration and power consumption decrease with increase in the number of aeration tank compartments. 2. This finding is consistent with operational data such as surplus sludge production, which increases as the number of compartments increases, and the DO levels in the final compartments. 3. There is a minimum biomass which is needed to fully use the available oxygen supply in the last compartment of a plant. Any extra is anoxic and so takes no part in the purification. This critical biomass is in direct proportion to the rate of aeration; decreases with increase in the number of compartments and increases with decrease in effluent substrate. 4. The Michaelis half saturation constant for substrate oxidation determined respirometrically with vigorous agitation gives a better fit with the variation of biomass in the Manchester full scale plants than the much lower Monod half saturation constant for quoted in ASM1. It appears that the extra turbulence increases the floc surface area so that diffusion of oxygen and/or biomass involvement increases. 5. The anoxic conditions in the initial compartments can explain why simultaneous nitrification and denitrification can occur in nitrifying plants. Estimates of the aerobic fraction of the sludge in each compartment based on the theory could be used to quantify this effect. Acknowledgments Thanks are due to R. B. Tench and J. R Tench for the computer model and the organisation of the author s web site, respectively. REFERENCES ATV, German ATV-DVWK, Rules and standards. May 2000.

8 Avcioglu E, Orhon D, Sözen S. A new method for the assessment of endogenous respiration rate under aerobic and anoxic conditions. Water Sci Technol. 1998, 38(8/9), Dold, P. L., Ekama, G. A., Marais, G. vr. A general model for the activated sludge process. Prog. Wat. Tech. 12, 1980, Hearon, J. Z., Rate behaviour of metabolic systems. Physiological Review, 32, 1952, 499. Henze, M., Grady, C. P. L., Gujer, W, Marais,. G. V. R., Matsuo, T., Activated sludge model No. 1 Kroiss, H., Ruider, E., Comparison of the plug-flow and complete mixed activated sludge process. Prog. Wat. Tech. 8 (6), Lui, Y., Overview of some theoretical approaches for derivation of the Monod equation. Appl Microbiol Biotechnol 2007 (73) Lumb, C., Halifax Sewage Works. Communication on visit to works. J Inst. Swge. Purif. 1959, (2), 215. McNicholas, J., Tench, H. B., A review of recent activated sludge research at Manchester. J Inst. Swge. Purif. 1959, (4), Reproduced in Pasveer, A., Research on activated sludge, IV, Purification with intense aeration. Sew. and ind. Wastes, 26, (2), Tench, H. B., Application of theoretical principles to activated sludge plant operation. Paper 31, Conference on biological waste treatment, Manhattan College, Reproduced in Tench, H. B., Morton, A. Y., The application of enzyme kinetics to activated sludge research. J Inst. Swge. Purif. 1962, (5), Reproduced in Tench, H. B., Sludge activity and the activated sludge process. Wat. Pollut. Control 1968, (4), Reproduced in Reproduced in Tench, H. B., Practical aspects of the oxygen supply/sludge activity relationship. Wat. Sci. Tech. 33, (12), Tench, H. B., Evidence for a radical theory of heterotrophic kinetics in the activated sludge process. Prague Conference of IWA specialist group on design operation and economics of large wastewater treatment plants. Water Intelligence Online, Aug Tench, H. B., 2008a. Oxygen demand and optimum dissolved oxygen. Water Pollution Research Laboratory Annual Report, 1962, 14. Ziglio, G., Andreottola, G., Barbesti, S., Boschetti, G., Bruni, L., Foladori, P., and Villa, R. Assessment of activated sludge viability with flow cytometry. Water Research, 36, (2002), Appendix 1 The biomass in the MLSS varies due to the steady state requirement that the fractional net rate of growth of biomass has to equal the fractional rate of growth of inert matter in the sludge: X H b H X H X H which rationalises to: Thus, when increasing amounts of sludge are held in a plant and the inert matter, X I, becomes large compared to its rate of growth, the biomass tends to a maximum value given by: X H max X H b X H X I X I X H X H X I X I b H X I (7), so that the endogenous decay rate is given by: X H max. In ASM1 (Henze et al, 1986), the specific growth rate is given as: b H X H Y H H 1Y H r resp.ox, where r resp.ox is the specific rate of substrate oxidation and whilst the yield, Y H, is stated to be variable, a typical value is given as 0.67g cell COD formed. Substituting this in the equation gives a growth rate of biomass which is twice the rate at which the substrate mass is oxidised and from equation (7), the maximum biomass X Hmax is thus twice the substrate oxidation rate divided by the specific endogenous decay rate. As the oxygen demand for endogenous respiration is given by multiplying the biomass by this same rate constant, the maximum possible rate of endogenous respiration in a

9 plant, bx Hmax, is related to the yield factor and can be taken to be typically twice the rate of oxygen consumption for substrate oxidation. The respirometric decay rate has been found to be 0.116d -1 by Ziglio et al (2002) and 0.092d -1 by Avcioglu et al (1998). For heterotrophic oxidation a sludge age of 3 days is recommended by the ATV, (2000), and this, at an average decay rate of 0.1d -1 and the typical maximum endogenous rate, gives an endogenous respiration rate equal to the substrate oxidation rate so that on this basis F may be taken to be 1.0. The only measurement of specific decay rate at Manchester gave a figure of about 0.14d -1, and thus it could be that the endogenous respiration ratio to the substrate oxidation demand was somewhat higher than this. Fundamentally the biomass needed to oxidise the substrate load is determined by the Michaelis- Menten relationship and varies according to the effluent quality in the last compartment of a plant. From equation (1) restated as: K m S E it can be seen that as S E decreases the ratio, X H, also decreases and thus increases. Theoretically, the ratio can be determined from the respirometric determinations of oxygen uptake used to measure K m and the maximum velocity, V, but the presence of stored substrate is a complication which makes it difficult to put a precise figure to the value of F. Appendix 2 It is known that enzymes combine with substrates to form intermediate unstable complexes which break down to give the products of the reaction. Thus: k 1 [E][S] = k 2 [ES], where E is an enzyme and S is a substrate and all concentrations are expressed in molar terms. The irreversible breakdown of this complex gives the products of the reaction and the rate of the reaction, v, is given by: v=k 3 [ES]. The Michaelis-Menten equation is derived by assuming that the substrate concentration is so much in excess of the enzyme that the concentration of the applied substrate is substantially unchanged when it is mixed with the enzyme. Applying this alters the equilibrium equation to: k 1 [E-ES][S] = k 2 [ES] and combining this with the equation giving the velocity of the reaction gives a steady state equilibrium of: k 1 [E-ES][S] = (k 2 +k 3 )[ES], which rationalises to the Michaelis-Menten equation: v K VS m S where the velocity v=k 3 [ES] and V is the maximum velocity attained when the enzyme is fully saturated with substrate and K m is the Michaelis constant which equals k 1 and is the substrate concentration at which the velocity is half the maximum. At low substrate concentrations, when K m is relatively large, the reaction rate approximates to first order. Pasveer s hypothesis that the low oxygen uptake at low turbulence is due to a low aerobic fraction in the sludge, could account for the differences in the reported values for this half saturation constant. As the breakdown of the substrate/biomass complex is the stage in the process which is dependent on the presence of oxygen, in oxygen limiting conditions the rate constant, k 3, has to be modified by multiplying it by the aerobic fraction, aer, and inserting this in the equivalence for K m gives k 2 aer k 3 k 1 k 2 k 3 X HS X H F bx H k 3 X HS S E so that a low value is obtained when turbulence is low. It also follows that an equally low value is obtained for the maximum velocity of reaction, V. If the effect of increased turbulence is mainly due to an increase in the floc surface area, then this is equivalent to an increase in the enzyme taking part in the reaction. This would lead to an increase in ES and an increase in rate of reaction so that the rate constant k 3 would appear to increase, as would K m and V. X HS